A new tool measures the distance between phonon collisions

Tabletop setup provides more nuanced picture of heat production in microelectronics.

Today’s computer chips pack billions of tiny transistors onto a plate of silicon within the width of a fingernail. Each transistor, just tens of nanometers wide, acts as a switch that, in concert with others, carries out a computer’s computations. As dense forests of transistors signal back and forth, they give off heat — which can fry the electronics, if a chip gets too hot.

Manufacturers commonly apply a classical diffusion theory to gauge a transistor’s temperature rise in a computer chip. But now an experiment by MIT engineers suggests that this common theory doesn’t hold up at extremely small length scales. The group’s results indicate that the diffusion theory underestimates the temperature rise of nanoscale heat sources, such as a computer chip’s transistors. Such a miscalculation could affect the reliability and performance of chips and other microelectronic devices.

“We verified that when the heat source is very small, you cannot use the diffusion theory to calculate temperature rise of a device. Temperature rise is higher than diffusion prediction, and in microelectronics, you don’t want that to happen,” says Professor Gang Chen, head of the Department of Mechanical Engineering at MIT. “So this might change the way people think about how to model thermal problems in microelectronics.”

The group, including graduate student Lingping Zeng and Institute Professor Mildred Dresselhaus of MIT, Yongjie Hu of the University of California at Los Angeles, and Austin Minnich of Caltech, has published its results this week in the journal Nature Nanotechnology.

Phonon mean free path distribution

Chen and his colleagues came to their conclusion after devising an experiment to measure heat carriers’ “mean free path” distribution in a material. In semiconductors and dielectrics, heat typically flows in the form of phonons — wavelike particles that carry heat through a material and experience various scatterings during their propagation. A phonon’s mean free path is the distance a phonon can carry heat before colliding with another particle; the longer a phonon’s mean free path, the better it is able to carry, or conduct, heat.

As the mean free path can vary from phonon to phonon in a given material — from several nanometers to microns — the material exhibits a mean free path distribution, or range. Chen, the Carl Richard Soderberg Professor in Power Engineering at MIT, reasoned that measuring this distribution would provide a more detailed picture of a material’s heat-carrying capability, enabling researchers to engineer materials, for example, using nanostructures to limit the distance that phonons travel.

The group sought to establish a framework and tool to measure the mean free path distribution in a number of technologically interesting materials. There are two thermal transport regimes: diffusive regime and quasiballistic regime. The former returns the bulk thermal conductivity, which masks the important mean free path distribution. To study phonons’ mean free paths, the researchers realized they would need a small heat source compared with the phonon mean free path to access the quasiballistic regime, as larger heat sources would essentially mask individual phonons’ effects.

Creating nanoscale heat sources was a significant challenge: Lasers can only be focused to a spot the size of the light’s wavelength, about one micron — more than 10 times the length of the mean free path in some phonons. To concentrate the energy of laser light to an even finer area, the team patterned aluminum dots of various sizes, from tens of micrometers down to 30 nanometers, across the surface of silicon, silicon germanium alloy, gallium arsenide, gallium nitride, and sapphire. Each dot absorbs and concentrates a laser’s heat, which then flows through the underlying material as phonons.

In their experiments, Chen and his colleagues used microfabrication to vary the size of the aluminum dots, and measured the decay of a pulsed laser reflected from the material — an indirect measure of the heat propagation in the material. They found that as the size of the heat source becomes smaller, the temperature rise deviates from the diffusion theory.

They interpret that as the metal dots, which are heat sources, become smaller, phonons leaving the dots tend to become “ballistic,” shooting across the underlying material without scattering. In these cases, such phonons do not contribute much to a material’s thermal conductivity. But for much larger heat sources acting on the same material, phonons tend to collide with other phonons and scatter more often. In these cases, the diffusion theory that is currently in use becomes valid.

A detailed transport picture

For each material, the researchers plotted a distribution of mean free paths, reconstructed from the heater-size-dependent thermal conductivity of a material. Overall, they observed the anticipated new picture of heat conduction: While the common, classical diffusion theory is applicable to large heat sources, it fails for small heat sources. By varying the size of heat sources, Chen and his colleagues can map out how far phonons travel between collisions, and how much they contribute to heat conduction.

Zeng says that the group’s experimental setup can be used to better understand, and potentially tune, a material’s thermal conductivity. For example, if an engineer desires a material with certain thermal properties, the mean free path distribution could serve as a blueprint to design specific “scattering centers” within the material — locations that prompt phonon collisions, in turn scattering heat propagation, leading to reduced heat carrying ability. Although such effects are not desirable in keeping a computer chip cool, they are suitable in thermoelectric devices, which convert heat to electricity. For such applications, materials that are electrically conducting but thermally insulating are desired.

“The important thing is, we have a spectroscopy tool to measure the mean free path distribution, and that distribution is important for many technological applications,” Zeng says.

This research was funded in part by in part by MIT’s Solid-State Solar Thermal Energy Conversion Center, which is funded by U.S. Department of Energy.

Source: http://newsoffice.mit.edu/2015/measuring-distance-between-phonon-collisions-0601

A magnetic field can steer sound? Regulate heat? Ohio State researchers prove phonons have magnetic properties

A team led by Ohio State’s Wolfgang Windl, Ph.D., used OSC’s Oakley Cluster to calculate acoustic phonon movement within an indium-antimonide semiconductor under a magnetic field. Their findings show that phonon amplitude-dependent magnetic moments are induced on the atoms, which change how they vibrate and transport heat.

Phonons—the elemental particles that transmit both heat and sound—have magnetic properties, according to a landmark study supported by Ohio Supercomputer Center (OSC) services and recently published by a researcher group from The Ohio State University.

In a recent issue of the journal Nature Materials, the researchers describe how a magnetic field, roughly the size of a medical MRI, reduced the amount of heat flowing through a semiconductor by 12 percent. Simulations performed at OSC then identified the reason for it—the magnetic field induces a diamagnetic response in vibrating atoms known as phonons, which changes how they transport heat.

“This adds a new dimension to our understanding of acoustic waves,” said Joseph Heremans, Ph.D., Ohio Eminent Scholar in Nanotechnology and a professor of mechanical engineering at Ohio State whose group performed the experiments. “We’ve shown that we can steer heat magnetically. With a strong enough magnetic field, we should be able to steer sound waves, too.”

People might be surprised enough to learn that heat and sound have anything to do with each other, much less that either can be controlled by magnets, Heremans acknowledged. But both are expressions of the same form of energy, quantum mechanically speaking. So any force that controls one should control the other.

The nature of the effect of the magnetic field initially was not understood and subsequently was investigated through computer simulations performed on OSC’s Oakley Cluster by Oscar Restrepo, Ph.D., a research associate, Nikolas Antolin, a doctoral student, and Wolfgang Windl, Ph.D., a professor, all of Ohio State’s Department of Materials Science and Engineering. After painstakingly examining all possible magnetic responses that a non-magnetic material can have to an external field, they found that the effect is due to a diamagnetic response, which exists in all materials. This suggests then that the general effect should be present in any solid.

The implication: in materials such as glass, stone, plastic—materials which are not conventionally magnetic—heat can be controlled magnetically, if you have a powerful enough magnet. This development may have future impacts on new energy production processes.
But, there won’t be any practical applications of this discovery any time soon: seven-tesla magnets like the one used in the study don’t exist outside of hospitals and laboratories, and a semiconductor made of indium antimonide had to be chilled to -450 degrees Fahrenheit (-268 degrees Celsius)—very close to absolute zero—to make the atoms in the material slow down enough for the phonons’ movements to be detectible.
To simulate the experiment, Windl and his computation team employed a quantum mechanical modeling strategy known as density functional theory (DFT). The DFT strategy was used to determine how the electron distribution changed when atoms vibrated with or without magnetic field. The motion of the electrons around their atoms changed in the field, creating diamagnetic moments when phonons were present. These moments then reacted to the field and slowed the heat transport, similar to an eddy current brake in a train.
The simulations were conducted on the Oakley Cluster, an HP/Intel Xeon system with more than 8,300 processor cores to provide researchers with a peak performance of 154 Teraflops—tech-speak for 154 trillion calculations per second. Since atoms can vibrate in many different ways, a large number of simulations were necessary, consuming approximately 1.5 million CPU hours even on a machine as powerful as Oakley. OSC engineers also helped the research team use OSC’s high-throughput, parallel file system to handle the immense datasets generated by the DFT model.

“OSC offered us phenomenal support; they supported our compilation and parallel threading issues, helped us troubleshoot hardware issues when they arose due to code demands, and moved us to the Lustre high-performance file system after we jammed their regular file system,” said Antolin, who is the expert for high-demand computations in Windl’s group.
“Dr. Windl and his team are important OSC clients, and we’re always pleased to support their research projects with our hardware, software and staff support services,” said David Hudak, Ph.D., OSC’s director of supercomputer services. “With the addition of the Ruby Cluster this past fall and another, much more powerful system upcoming this fall, OSC will continue to offer even larger, faster and more powerful services to support this type of discovery and innovation.”
Next, the group plans to test whether they can deflect sound waves sideways with magnetic fields.
Coauthors on the study included graduate student Hyungyu Jin and postdoctoral researcher Stephen Boona from mechanical and aerospace engineering; and Roberto Myers, Ph.D., an associate professor of materials science and engineering, physics and mechanical and aerospace engineering.
Funding for the study came from the U.S. Army Research Office, the U.S. Air Force Office of Scientific Research and the National Science Foundation (NSF), including funds from the NSF Materials Research Science and Engineering Center at Ohio State. Computing services were provided by the Ohio Supercomputer Center.

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Note: Significant portions of this story were adapted from a release written earlier by Pam Frost Gorder in the Research & Innovation Communications office at The Ohio State University: https://news.osu.edu/news/2015/03/23/heatmag/(link sends e-mail)

The Ohio Supercomputer Center (OSC), a member of the Ohio Technology Consortium of the Ohio Board of Regents, addresses the rising computational demands of academic and industrial research communities by providing a robust shared infrastructure and proven expertise in advanced modeling, simulation and analysis. OSC empowers scientists with the vital resources essential to make extraordinary discoveries and innovations, partners with businesses and industry to leverage computational science as a competitive force in the global knowledge economy, and leads efforts to equip the workforce with the key technology skills required to secure 21st century jobs. For more, visit www.osc.edu.

Researchers Find Unambiguous Evidence for Coherent Phonons in Superlattices

Surface topography of a 200 nanometer thick
strontium titanate/ calcium titanate superlattice
film on a strontium titanate substrate.

We all learn in high school science about the dual nature of light – that it exists as both waves and quantum particles called photons. It is this duality of light that enables the coherent transport of photons in lasers. 

Sound at the atomic-scale has the same dual nature, existing as both waves and quasi-particles known as phonons. Does this duality allow for phonon-based lasers? Some theorists say yes, but the point has been argued for years. Recently a large collaboration, in which Berkeley Lab scientists played a prominent role, provided the first “unambiguous demonstration” of the coherent transport of phonons.

Ramamoorthy Ramesh, a senior scientist with Berkeley Lab’s Materials Sciences Division, was a co-leader with Arun Majumdar, a former Associated Laboratory director at Berkeley Lab and currently VP for Energy at Google, of an experiment in which phonons underwent particle-to-wave crossovers in superlattices of perovskite oxides.

“Our observations open up new opportunities for studying the wave-like nature of phonons, particularly phonon interference effects,” says Ramesh. “Such research should have potential applications in thermoelectrics and thermal management, and in the long run could help the development of phonon lasers.”

Unlike elementary particles such as electrons and photons, whose wave nature and coherent properties are well-established, experimental demonstration of coherent wave-like properties of phonons has been limited. This is because phonons are not true particles, but the collective vibrations of atoms in a crystal lattice that can be quantized as if they were particles. However, understanding the coherent wave nature of phonons is of fundamental importance to thermoelectrics, materials that can convert heat into electricity, or electricity into heat, which represent a potentially huge source of clean, green energy.

“Lower thermal conductivity is one of the keys to improving the efficiency of thermoelectric materials and the key to thermal conductivity in semiconductors is phonon transport,” Majumdar says. “Nanostructures such as superlattices are the ideal model systems for the study of phonon transport, particularly the wave-particle crossover, because the wavelength of the most relevant phonons are in the range of one to 10 nanometers.”

Electron microscopy-spectroscopy images of a strontium titanate/barium titanate superlattice film reveal the presence of atomically sharp interfaces with minimal intermixing. Superlattice is color-coded with strontium (orange) barium (purple) and titanium (green).

Superlattices are artificial periodic structures consisting of  two dissimilar semiconductors in alternating layers a few nanometers thick. For this demonstration, the collaboration synthesized high-quality superlattices of electrically insulating perovskite oxides on various single-crystal oxide substrates. Interface densities in these superlattices were systematically varied using two different epitaxial growth techniques. Thermal conductivity was measured as a function of interface density.

“Our results were in general agreement with theoretical predictions of crossover from incoherent particle-like to coherent wave-like phonon transport,” Ramesh says. “We also found sufficient evidence to eliminate extraneous or spurious effects, which could have alternatively explained the observed thermal conductivity minimum in these superlattices.”

Capitalizing on the wave behavior of phonons should enable new advances in new heat transfer applications, the collaborators say. Furthermore, perovskite superlattice-based heterostructures could also serve as basic building blocks for the development of lasers in which beams of coherent phonons rather than coherent photons are emitted. Phonon lasers could provide advanced ultrasound imaging or highly accurate measuring devices, among other possibilities.

Ramesh is a corresponding author of a Nature Materials paper describing this research titled “Crossover from incoherent to coherent phonon scattering in epitaxial oxide superlattices.”

This research was primarily supported by U.S. Department of Energy’s Office of Science.

Source: http://newscenter.lbl.gov/science-shorts/2014/02/05/coherent-phonons-in-superlattices/